[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Frequency-Severity Method** ## Definition ==Frequency-Severity Method== is a reserving approach that separately projects ultimate claim counts (frequency) and average cost per claim (severity), then multiplies them to estimate ultimate losses. ## Formula ``` Ultimate Losses = Ultimate Claim Count × Ultimate Severity Where: Ultimate Claim Count = from claim count triangle development Ultimate Severity = Ultimate Losses / Ultimate Claims (from experience) ``` ## Methodology ### Step 1: Develop Claim Counts ``` Create claim count triangle Apply development factors Project ultimate claim counts ``` ### Step 2: Estimate Ultimate Severity ``` Options: a) Historical average severity by year b) Trended current severity c) Expected severity from pricing d) Development of paid per claim ``` ### Step 3: Calculate Ultimate Losses ``` Ultimate = Ultimate Claims × Ultimate Severity IBNR = Ultimate - Reported ``` ## Complete Example ``` AY 2023 @ 12 months: Claim Count Data: Reported counts: 500 12-Ult count CDF: 1.200 Ultimate counts: 500 × 1.200 = 600 claims Severity Estimate: Historical avg severity (trended): $8,500 Or: Current severity trend suggests $8,500 Ultimate Losses: = 600 claims × $8,500 per claim = $5,100,000 Reported Losses: $3,400,000 IBNR: $5,100,000 - $3,400,000 = $1,700,000 ``` ## Advantages - Separates frequency and severity trends - Can incorporate external trend information - Useful when frequency/severity change independently - Provides additional insights ## Disadvantages - Requires claim count data - More complex than basic methods - Severity estimation can be challenging - Assumes independence of frequency/severity ## When to Use **Preferred when:** - Claim counts available and reliable - Frequency and severity trends differ - Want to incorporate trend assumptions - Need to understand drivers of loss changes **Example situations:** - Frequency declining but severity increasing - Need to reflect different trend assumptions - Large variability in claim sizes - Want to validate other methods ## Related Concepts - [[Frequency Analysis#Definition]] - [[Severity Analysis#Definition]] - [[Claim Count Triangle#Definition]] ## References - Friedland, Chapter 8